Does it work if you try it on the admin demo page: https://ajaxsearchpro.com/admin-demo/
If it works there, then try reinstalling the plugin via the plugin manager, there might be corrupted files.
If it does not work on the demo site either, then there might be an issue in your browser. Try turning off some browser addons, which may interfeere with the scripts.
Feel free to add temporary back-end details, and I will take a look at the issue.